I am visiting for one evening and need an inexpensive hotel in or convenient to Dupont Circle, someplace where a single woman would feel safe; wi fi a must.
Thanks.

please define "inexpensive"

I recently stayed at the St.Gregory Hotel and Suites, it's about 4 blocks from Dupont Circle.I was there for leisure and did a lot of walking, I found this area to be extremely safe.The rooms were very spacious with a comfortable King size bed. Be aware that if you are driving here there is a $29/night valet charge but you will find that at any downtown DC hotel.
http://www.capitalhotelswdc.com/StGregoryHotelWDC_com/

Thanks! I will be taking amtrak so valet is a non-issue.
Inexpensive? Under $150.

$150 is going to tough on a weekday, much easier on a weekend.

wi-fi at Starbucks 1 block away, but this Dupont hotel has rooms under $150.

http://www.tabardinn.com/

Sometimes Helix Hotel has some really good deals. It is located at 1430 Rhode Island Avenue, NW and is a little over a half mile from the Circle but in looking for hotels for my boss' clients, this place has always had the best deals (during the week also)

It is hit or miss and it might be further from Dupont Circle than you want to be but if cost is most important, it might be good. It don't know anything about wi-fi

Weekend or weekday?

There are several Kimpton Hotels in the area. They offer a 'Ride the rails' promotional rate which is a pretty good deal if you're coming by train. I have the Topaz Hotel booked for next weekend at $129 + taxes per night, the rails promotion coupled with a AAA rate. This is my first time at Topaz; I normally stay at Madera.

If you go with a Kimpton hotel, sign up for their frequent guest program ahead of time to take advantage of free WiFi.

Consider using Priceline. I was able to secure a room last spring at the Marriott Mayflower (near Dupont Circle) for $70/night.

I can vouch that the Tabard Inn is very charming, if you like non-corporate, b&b style inns. Funky, a bit creaky, and charming. The restaurant there is very good too!